Simple Harmonic Motion

Define displacement, x

distance from equilibrium position

Define amplitude, A

maximum displacement

Define time period, T

time taken for one full oscillation

Define frequency, f

number of oscillations per unit time

Define phase difference, ϕ

the fraction of an oscillation between two oscillating objects

Define angular frequency, ω

rate of change of angle

Define simple harmonic motion

oscillation where acceleration of the oscillator is directly proportional to the displacement from equilibrium, and acts towards equilibrium

State the key equation of SHM

a=-ω²x

State the relationship between period and amplitude

period is completely independent

Explain an experiment to investigate period and frequency

Set the oscillator into motion, using a stopwatch to measure time taken for n oscillations, then divide by n.

State the equations for displacement in SHM

x = Acosωt x = Asinωt

where sin is used if starting at equilibrium position, and cos at amplitude position

Where does maximum velocity and acceleration occur?

v_max occurs at equilibrium, whereas a_max occurs at amplitude points

state the equation for velocity in SHM

v = +-ω(sqrt(A²-x²))

State the equation for v_max

x = 0, therefore v_max = ωA

a_max = ω²A

Explain energy exchange during SHM

Maximum kinetic energy occurs at equilibrium point, where v is max, maximum Gpotential energy occurs at amplitude positions, where x is max

Explain damping

the process by which the amplitude of oscillations decreases over time, due to energy lost to resistive forces

Explain resonance

When the driving frequency is the same as the natural frequency, resonance occurs and the amplitude of oscillation rapidly increases if there is no damping until failure